1. Field of the Invention
The present invention relates to the characterization of nonlinear circuits/systems, and particularly to a nonlinear systems measurement system and method.
2. Description of the Related Art
Electronic circuits built around active devices are inherently nonlinear. While this inherent nonlinearity may be considered as a disadvantage, for example, in amplifiers and filters, in some applications designers are trying to optimize their circuits to provide nonlinearities (for example, in mixers and detectors). Of particular interest here is the characterization of electronic circuits/systems exhibiting nonlinearities with even and odd symmetries. Whenever a signal comprising multi-sinusoids is applied to the input of an electronic circuit with even and odd symmetries, the output usually comprises a wide range of harmonics, including sums and differences of the original input frequencies and their harmonics, that is, intermodulation products.
For example, in designing a mixer or a down-converter, the output frequency of interest would be the difference between two input frequencies, while in designing an up-converter, the output frequency of interest would be the sum of two input frequencies. In all cases, it is useful for the designer to have a quick indication of the likely spectrum of output components, including the harmonics and intermodulation products, from a nonlinear electronic circuit/system exhibiting even and odd symmetries when excited by a multi-sinusoidal input signal. This requires a tractable mathematical model for the instantaneous input-output characteristics of the nonlinear electronic circuit/system under consideration.
While a Taylor series-based model is the most straightforward approach for modeling nonlinear characteristics with even- and odd-symmetry nonlinearities, it is useful only when the nonlinearity under consideration contains relatively low orders of distortion, thus allowing the truncation of the Taylor series after a relatively small number of terms. However, nonlinear electronic circuits/systems with hard even and odd symmetries require large numbers of the Taylor series expansion. The parameters of the Taylor series expansion are usually obtained using curve-fitting techniques, with the relative root-mean-square (RRMS) error used as a criterion for deciding the required accuracy of the Taylor series-based model. Increasing the number of terms of the Taylor-series expansion does not necessarily improve the accuracy of the model. In fact, increasing the number of terms may improve the accuracy of the model at or near the original data points, but in between the original data points the fitted curve may oscillate. Thus, a high order Taylor-series model may yield an acceptable RRMS error, when comparing the fitted curve with the original input data, but it may not yield reliable prediction for the harmonic and intermodulation performance of the electronic circuit/system under consideration.
The basic assumption of the methods used to predict the harmonic and intermodulation performance of nonlinear electronic circuits is that the instantaneous input-output transfer characteristic is available. Unfortunately, for practical reasons, this characteristic is not always available, especially at relatively high frequencies where nonlinear circuits/systems are usually characterized by their input-power-output-power characteristic. Obviously, the input-power-output-power characteristic cannot be used for predicting the harmonic and intermodulation performance of nonlinear circuits/systems excited by multisinusoidal input signals. Thus, recourse to the inverse process, that is, predicting the instantaneous characteristic from the measured harmonic or intermodulation performance, would be necessary to obtain the instantaneous characteristic. This would require the use of surface-fitting techniques, especially when a large number of the Taylor series terms are used for modeling the nonlinear characteristics.
From the above discussion it appears that a simple mathematical model that can be easily used for predicting the amplitudes of the harmonics and intermodulation products of a nonlinear electronic circuit/system with even and odd symmetries excited by a multisinusoidal signal is needed.
Thus, a nonlinear systems measurement system and method solving the aforementioned problems is desired.